We define the oscillator and Coulomb systems on four-dimensional spaces with
U(2)-invariant Kahler metric and perform their Hamiltonian reduction to the
three-dimensional oscillator and Coulomb systems specified by the presence of
Dirac monopoles. We find the Kahler spaces with conic singularity, where the
oscillator and Coulomb systems on three-dimensional sphere and two-sheet
hyperboloid are originated. Then we construct the superintegrable oscillator
system on three-dimensional sphere and hyperboloid, coupled to monopole, and
find their four-dimensional origins. In the latter case the metric of
configuration space is non-Kahler one. Finally, we extend these results to the
family of Kahler spaces with conic singularities.